Paper Together: sit a paper in a room with your friends.See how it works
This page sets out the method for scatter graphs in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Scatter graphs topic page.
When asked 'describe the correlation' or 'describe the relationship'.
When asked to estimate a value using the graph.
Each point is one pair of measurements.
An outlier sits away from the cloud and can pull a line of best fit.
Upwards is positive. Downwards is negative. No tilt is none.
Describe the strength only if the question asks: strong if the points hug the line, weak if they are spread out.
A straight line through the middle of the points, following their tilt.
There should be points on both sides. It does not have to pass through the origin.
Draw up or across from a value to the line, then read the other axis.
Say it is an estimate. The line is a summary, not every point.
Reading inside the data is safer than reading far beyond it.
Beyond the data, the pattern may change.
Ice-cream sales and temperature can both rise together without one being drawn as the cause on the graph.
The graph shows association. A cause needs a reason beyond the points.
Read the cloud from left to right, which is the direction x increases. If the points climb, larger x goes with larger y. That is positive correlation. Hours of revision and test scores often look like this. The points do not have to sit on a perfect line. A clear upward drift is enough.
If the points fall as you look right, larger x goes with smaller y. That is negative correlation. The time left before a bus and the distance you still have to run can behave like this. No correlation means the heights of the points do not drift up or down. A blob, or a flat scatter, is none. Do not force a slope onto a cloud that does not have one.
Method: 1. Look from left to right, the direction x increases. 2. Call a rising cloud positive correlation and a falling cloud negative. 3. No steady rise or fall means no correlation. 4. Describe the pattern. Do not say one variable causes the other just because the cloud slopes.
A line can be strong and the cause can still be somewhere else. Two things can share a hidden third factor, or the link can be a coincidence in a small sample. The graph only shows that the pairs line up. Cause needs a reason about the situation, and even then you say "this suggests", not "this proves".
An outlier is a point far from the rest. One student who revised for ages and still scored very low sits off a positive cloud. You mention it. You do not let one point rename the correlation, and you do not delete it unless the question says it was recorded wrongly. Outliers are part of describing the graph honestly.
Method: 1. State the type of correlation first. 2. Do not write that one variable causes the other unless the question gives a reason beyond the points. 3. Name an outlier if one point is far from the pattern. 4. Keep the outlier in the description. Do not pretend the cloud is perfect.
When the question gives y = 2x + 3, the estimate is arithmetic. Put the given x into the right-hand side. For x = 4, y = 2 × 4 + 3 = 11. The 2 is the step of the line: each extra unit of x adds 2 to y. The 3 is the value of y when x is 0, which may sit outside the data.
Swap the letters only if you are asked for x given y. Then you solve the equation. Most estimate questions give x and want y, so substitute, multiply, then add or subtract the constant. A negative constant, as in y = 5x - 8, is still just substitution. Do the multiplication before you subtract.
Method: 1. Copy the equation and the x value you were given. 2. Replace x, then multiply before you add or subtract. 3. State the result as the estimate of y, using the units of y. 4. If you are asked for x, solve the equation instead of substituting into the wrong side.
Interpolation means the x you use sits between the smallest and largest x that were plotted. The line is a summary of points you have actually seen, so the estimate is the better kind. If the data run from x = 2 to x = 9, then x = 4 and x = 7 are both interpolation.
Extrapolation means you have gone past the ends. The straight line might bend, or stop meaning anything, outside the cloud. An estimate at a far x can still be calculated from the equation, and you should still calculate it if asked, but you say it is less reliable. The arithmetic can be perfect and the prediction can still be poor. Reliability is about the data, not about your multiplying.
Method: 1. Write down the smallest and largest x in the data. 2. If your x is between them, call the estimate interpolation. 3. If your x is outside them, call it extrapolation and say it is less reliable. 4. Finish the substitution, then add the warning about the range of the data.
Exam questions often say "Describe the correlation" or "Circle the strength and type of correlation". Give two words. The type is positive, negative or none. The strength is strong if the points sit close to a straight line and weak if they are spread out. So the answer is something like "weak negative" or "strong positive".
The question may then ask you to describe the relationship in words. Write a full sentence that uses the real quantities: "As the age of the car increases, the value of the car decreases". Do not just repeat the word "negative". Steepness is not strength. A steep line of points that are scattered is still weak.
Method: 1. Look at how the points run from left to right: up is positive, down is negative. 2. Judge how close the points are to a straight line: close is strong, spread out is weak. 3. Give the type and strength together, for example strong positive. 4. If asked for the relationship, write "As (first thing) increases, (second thing) increases or decreases".
Tip: If the points form a curve or a shapeless cloud, there is no linear correlation. Say "no correlation" and stop.
To estimate from a line you substitute. For y = 3x + 2 and x = 7, the estimate is 3 × 7 + 2 = 23. To go the other way, set y equal to the value you were given and solve for x. Always match the letters to the quantities in the question: which one is on the horizontal axis and which is on the vertical axis.
A harder question asks what the numbers in the equation mean. The gradient is the change in y for each increase of 1 in x. The y-intercept is the value of y when x = 0, but it can be meaningless if x = 0 is far outside the data. Write your answer in context, for example "each extra kilometre adds 6 minutes".
Method: 1. Read the equation and note which letter is the quantity you are given. 2. Substitute that value, or set y equal to it and solve. 3. Round sensibly and give the unit. 4. For meaning, say what the gradient is per unit and what the intercept is when the first quantity is zero.
An outlier is a point that does not follow the pattern of the others. A question may say "One point is an outlier. Write down its coordinates" and then "Give a possible reason". Tell the reader what makes it odd, for example "a very old car with a high price might be rare". Outliers can be left out when you draw the line of best fit.
Estimates inside the range of the data are interpolation and are fairly reliable. Estimates outside the range are extrapolation and may be wrong, because the pattern might not carry on. If a line gives an impossible value, such as a negative price, say so. A typical exam mark is for writing that the line is only valid for the range of the data.
Method: 1. Check the range of x values in the data before you use the line. 2. If your x is outside the range, state that the estimate is extrapolation and may not be reliable. 3. Check whether the answer makes sense, for example a time or price cannot be negative. 4. For an outlier, write down its coordinates and a reason it may be unusual.
Tip: Use the words "outside the range of the data" in your answer. They show you have understood the limit.
A good line of best fit passes through the mean point (barx, bary), where barx is the mean of the x values and bary is the mean of the y values. If you are given the gradient m, put the mean point in y = mx + c and solve for c. For barx = 4, bary = 11 and m = 2, we get c = 11 - 8 = 3.
You may also be given two points on the line. Find the gradient with change in y over change in x, then substitute one point to find c. State the equation and use it for the estimate. Show each step because a slip in c will carry into the estimate.
Method: 1. Add the x values and divide by how many there are, then do the same for y. 2. Write y = mx + c with the gradient you know. 3. Substitute the mean point or a given point to find c. 4. Use the finished equation to estimate, and check it passes through the point you used.
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